Simplify the following expression: $ z = \dfrac{-5}{2} + \dfrac{-1}{-5k + 2} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{-5k + 2}{-5k + 2}$ $ \dfrac{-5}{2} \times \dfrac{-5k + 2}{-5k + 2} = \dfrac{25k - 10}{-10k + 4} $ Multiply the second expression by $\dfrac{2}{2}$ $ \dfrac{-1}{-5k + 2} \times \dfrac{2}{2} = \dfrac{-2}{-10k + 4} $ Therefore $ z = \dfrac{25k - 10}{-10k + 4} + \dfrac{-2}{-10k + 4} $ Now the expressions have the same denominator we can simply add the numerators: $z = \dfrac{25k - 10 - 2}{-10k + 4} $ $z = \dfrac{25k - 12}{-10k + 4}$ Simplify the expression by dividing the numerator and denominator by -1: $z = \dfrac{-25k + 12}{10k - 4}$